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Simplifying 2(3r + 1) + 6 = 5(-2r + -8) Reorder the terms: 2(1 + 3r) + 6 = 5(-2r + -8) (1 * 2 + 3r * 2) + 6 = 5(-2r + -8) (2 + 6r) + 6 = 5(-2r + -8) Reorder the terms: 2 + 6 + 6r = 5(-2r + -8) Combine like terms: 2 + 6 = 8 8 + 6r = 5(-2r + -8) Reorder the terms: 8 + 6r = 5(-8 + -2r) 8 + 6r = (-8 * 5 + -2r * 5) 8 + 6r = (-40 + -10r) Solving 8 + 6r = -40 + -10r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10r' to each side of the equation. 8 + 6r + 10r = -40 + -10r + 10r Combine like terms: 6r + 10r = 16r 8 + 16r = -40 + -10r + 10r Combine like terms: -10r + 10r = 0 8 + 16r = -40 + 0 8 + 16r = -40 Add '-8' to each side of the equation. 8 + -8 + 16r = -40 + -8 Combine like terms: 8 + -8 = 0 0 + 16r = -40 + -8 16r = -40 + -8 Combine like terms: -40 + -8 = -48 16r = -48 Divide each side by '16'. r = -3 Simplifying r = -3
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